Question

by checking only the equation and the coefficients, determine the smallest and largest possible rational roots of the equation 2x^4+x^2-22x+8=0

Answer 1

2 x^4 + x^2 - 22 x + 8 = 0

possible rational roots  =  + or - of factors of 8 / + or - of factors of 2  =

One root by checking = 2
zero or root cannot be negative. LHS will be positive for -ve x.

Just by looking at the coefficients: maximum possible 8/2 and minimum possible 1/2
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 F(x) = A (x - C1)(x - C2) (x - C3) (x - C4)        polynomial of degree 4.
Multiply and form the polynomial.  In that, we will have the

Leading Coeffient of x^4 :  A
constant term : coefficient of x^0 :  A  C1 C2 C3 C4

So the possible rational zeros can be obtained by  : 
               + or - of factors of constant term / leading coefficient

Our case :  rational zero's  are possibly :  +-  factors of 8 / factors of 2 
                           :  8/2  , -8/2, +- 1, +-2 , +- 1/2